{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T04:31:38Z","timestamp":1750221098626,"version":"3.41.0"},"reference-count":10,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2019,1,17]],"date-time":"2019-01-17T00:00:00Z","timestamp":1547683200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["SIGMETRICS Perform. Eval. Rev."],"published-print":{"date-parts":[[2019,1,18]]},"abstract":"<jats:p>We consider a stochastic queueing system modelling the behaviour of a wireless network with nodes employing a discrete-time version of the standard decentralised medium access algorithm. The system is unsaturated \" each node receives an exogenous flow of packets at the rate ! packets per time slot. Each packet takes one slot to transmit, but neighbouring nodes cannot transmit simultaneously. The algorithm we study is standard in that: a node with empty queue does not compete for medium access; the access procedure by a node does not depend on its queue length, as long as it is non-zero. Two system topologies are considered, with nodes arranged in a circle and in a line. We prove that, for either topology, the system is stochastically stable under condition ! &lt; 2\/5. This result is intuitive for the circle topology as the throughput each node receives in a saturated system (with infinite queues) is equal to the so-called parking constant, which is larger than 2\/5. (This fact, however, does not help to prove our result.) The result is not intuitive at all for the line topology as in a saturated system some nodes receive a throughput lower than 2\/5.<\/jats:p>","DOI":"10.1145\/3305218.3305231","type":"journal-article","created":{"date-parts":[[2019,1,17]],"date-time":"2019-01-17T17:15:15Z","timestamp":1547745315000},"page":"33-35","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Stability of a standard decentralised medium access"],"prefix":"10.1145","volume":"46","author":[{"given":"Seva","family":"Shneer","sequence":"first","affiliation":[{"name":"Heriot-Watt University, Edinburgh, United Kingdom"}]},{"given":"Alexander","family":"Stolyar","sequence":"additional","affiliation":[{"name":"University of Illinois at Urbana-Champaign, Champaign, IL, USA"}]}],"member":"320","published-online":{"date-parts":[[2019,1,17]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1177004828"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2008.2011427"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1109\/TNET.2009.2035046"},{"key":"e_1_2_1_4_1","first-page":"199","article-title":"Ergodicity of Stochastic Processes Describing the Operation of Open Queueing Networks","volume":"28","author":"Rybko A.N.","year":"1992","unstructured":"A.N. Rybko and A.L. Stolyar ( 1992 ). Ergodicity of Stochastic Processes Describing the Operation of Open Queueing Networks . Problems of Information Transmission , 28 , 199 -- 220 . A.N. Rybko and A.L. Stolyar (1992). Ergodicity of Stochastic Processes Describing the Operation of Open Queueing Networks. Problems of Information Transmission, 28, 199--220.","journal-title":"Problems of Information Transmission"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1214\/11-AAP763"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.spl.2016.09.019"},{"key":"e_1_2_1_7_1","unstructured":"S. Shneer A. L. Stolyar. Stability conditions for a discrete-time decentralised medium access algorithm. Submitted. https:\/\/arxiv.org\/abs\/1707.01548  S. Shneer A. L. Stolyar. Stability conditions for a discrete-time decentralised medium access algorithm. Submitted. https:\/\/arxiv.org\/abs\/1707.01548"},{"issue":"4","key":"e_1_2_1_8_1","first-page":"491","article-title":"On the Stability of Multiclass Queueing Networks: A Relaxed Sufficient Condition via Limiting Fluid Processes","volume":"1","author":"Stolyar A.L.","year":"1995","unstructured":"A.L. Stolyar ( 1995 ). On the Stability of Multiclass Queueing Networks: A Relaxed Sufficient Condition via Limiting Fluid Processes . Markov Processes and Related Fields , 1 ( 4 ), 491 -- 512 . A.L. Stolyar (1995). On the Stability of Multiclass Queueing Networks: A Relaxed Sufficient Condition via Limiting Fluid Processes. Markov Processes and Related Fields, 1(4), 491--512.","journal-title":"Markov Processes and Related Fields"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1109\/9.182479"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.peva.2010.08.011"}],"container-title":["ACM SIGMETRICS Performance Evaluation Review"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3305218.3305231","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3305218.3305231","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T00:58:09Z","timestamp":1750208289000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3305218.3305231"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,17]]},"references-count":10,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,1,18]]}},"alternative-id":["10.1145\/3305218.3305231"],"URL":"https:\/\/doi.org\/10.1145\/3305218.3305231","relation":{},"ISSN":["0163-5999"],"issn-type":[{"type":"print","value":"0163-5999"}],"subject":[],"published":{"date-parts":[[2019,1,17]]},"assertion":[{"value":"2019-01-17","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}